Global pooling is one of the most significant operations in many machine learning models and tasks, which works for information fusion and structured data (like sets and graphs) representation. However, without solid mathematical fundamentals, its practical implementations often depend on empirical mechanisms and thus lead to sub-optimal, even unsatisfactory performance. In this work, we develop a novel and generalized global pooling framework through the lens of optimal transport. The proposed framework is interpretable from the perspective of expectation-maximization. Essentially, it aims at learning an optimal transport across sample indices and feature dimensions, making the corresponding pooling operation maximize the conditional expectation of input data. We demonstrate that most existing pooling methods are equivalent to solving a regularized optimal transport (ROT) problem with different specializations, and more sophisticated pooling operations can be implemented by hierarchically solving multiple ROT problems. Making the parameters of the ROT problem learnable, we develop a family of regularized optimal transport pooling (ROTP) layers. We implement the ROTP layers as a new kind of deep implicit layer. Their model architectures correspond to different optimization algorithms. We test our ROTP layers in several representative set-level machine learning scenarios, including multi-instance learning (MIL), graph classification, graph set representation, and image classification. Experimental results show that applying our ROTP layers can reduce the difficulty of the design and selection of global pooling -- our ROTP layers may either imitate some existing global pooling methods or lead to some new pooling layers fitting data better. The code is available at \url{https://github.com/SDS-Lab/ROT-Pooling}.

Microfinance, despite its significant potential for poverty reduction, is facing sustainability hardships due to high default rates. Although many methods in regular finance can estimate credit scores and default probabilities, these methods are not directly applicable to microfinance due to the following unique characteristics: a) under-explored (developing) areas such as rural Africa do not have sufficient prior loan data for microfinance institutions (MFIs) to establish a credit scoring system; b) microfinance applicants may have difficulty providing sufficient information for MFIs to accurately predict default probabilities; and c) many MFIs use group liability (instead of collateral) to secure repayment. Here, we present a novel control-theoretic model of microfinance that accounts for these characteristics. We construct an algorithm to learn microfinance decision policies that achieve financial inclusion, fairness, social welfare, and sustainability. We characterize the convergence conditions to Pareto-optimum and the convergence speeds. We demonstrate, in numerous real and synthetic datasets, that the proposed method accounts for the complexities induced by group liability to produce robust decisions before sufficient loans are given to establish credit scoring systems and for applicants whose default probability cannot be accurately estimated due to missing information. To the best of our knowledge, this paper is the first to connect microfinance and control theory. We envision that the connection will enable safe learning and control techniques to help modernize microfinance and alleviate poverty.

The hyperparameter optimization of neural network can be expressed as a bilevel optimization problem. The bilevel optimization is used to automatically update the hyperparameter, and the gradient of the hyperparameter is the approximate gradient based on the best response function. Finding the best response function is very time consuming. In this paper we propose CPMLHO, a new hyperparameter optimization method using cutting plane method and mixed-level objective function.The cutting plane is added to the inner layer to constrain the space of the response function. To obtain more accurate hypergradient,the mixed-level can flexibly adjust the loss function by using the loss of the training set and the verification set. Compared to existing methods, the experimental results show that our method can automatically update the hyperparameters in the training process, and can find more superior hyperparameters with higher accuracy and faster convergence.

Bayesian optimization (BO) is one of the most effective methods for closed-loop experimental design and black-box optimization. However, a key limitation of BO is that it is an inherently sequential algorithm (one experiment is proposed per round) and thus cannot directly exploit high-throughput (parallel) experiments. Diverse modifications to the BO framework have been proposed in the literature to enable exploitation of parallel experiments but such approaches are limited in the degree of parallelization that they can achieve and can lead to redundant experiments (thus wasting resources and potentially compromising performance). In this work, we present new parallel BO paradigms that exploit the structure of the system to partition the design space. Specifically, we propose an approach that partitions the design space by following the level sets of the performance function and an approach that exploits partially-separable structures of the performance function found. We conduct extensive numerical experiments using a reactor case study to benchmark the effectiveness of these approaches against a variety of state-of-the-art parallel algorithms reported in the literature. Our computational results show that our approaches significantly reduce the required search time and increase the probability of finding a global (rather than local) solution.

Simulating quantum channels is a fundamental primitive in quantum computing, since quantum channels define general (trace-preserving) quantum operations. An arbitrary quantum channel cannot be exactly simulated using a finite-dimensional programmable quantum processor, making it important to develop optimal approximate simulation techniques. In this paper, we study the challenging setting in which the channel to be simulated varies adversarially with time. We propose the use of matrix exponentiated gradient descent (MEGD), an online convex optimization method, and analytically show that it achieves a sublinear regret in time. Through experiments, we validate the main results for time-varying dephasing channels using a programmable generalized teleportation processor.

The concept of walkable urban development has gained increased attention due to its public health, economic, and environmental sustainability benefits. Unfortunately, land zoning and historic under-investment have resulted in spatial inequality in walkability and social inequality among residents. We tackle the problem of Walkability Optimization through the lens of combinatorial optimization. The task is to select locations in which additional amenities (e.g., grocery stores, schools, restaurants) can be allocated to improve resident access via walking while taking into account existing amenities and providing multiple options (e.g., for restaurants). To this end, we derive Mixed-Integer Linear Programming (MILP) and Constraint Programming (CP) models. Moreover, we show that the problem's objective function is submodular in special cases, which motivates an efficient greedy heuristic. We conduct a case study on 31 underserved neighborhoods in the City of Toronto, Canada. MILP finds the best solutions in most scenarios but does not scale well with network size. The greedy algorithm scales well and finds near-optimal solutions. Our empirical evaluation shows that neighbourhoods with low walkability have a great potential for transformation into pedestrian-friendly neighbourhoods by strategically placing new amenities. Allocating 3 additional grocery stores, schools, and restaurants can improve the "WalkScore" by more than 50 points (on a scale of 100) for 4 neighbourhoods and reduce the walking distances to amenities for 75% of all residential locations to 10 minutes for all amenity types. Our code and paper appendix are available at https://github.com/khalil-research/walkability.

Microchannel heat sinks are an efficient cooling method for semiconductor packages. However, to properly cool increasingly complex and thermally dense circuits, microchannel designs should be improved and expanded on. In this paper, microchannel designs with secondary channels and with ribs are investigated using computational fluid dynamics and are coupled with a multi-objective optimization algorithm to determine and propose optimal solutions based on observed thermal resistance and pumping power. A workflow that combines Latin hypercube sampling, machine learning-based surrogate modeling and multi-objective optimization is proposed. Random forests, gradient boosting algorithms and neural networks were considered during the search for the best surrogate. We demonstrated that tuned neural networks can make accurate predictions and be used to create an acceptable surrogate model. Optimized solutions show a negligible difference in overall performance when compared to the conventional optimization approach. Additionally, solutions are calculated in one-fifth of the original time. Generated designs attain temperatures that are lower by more than 10% under the same pressure limits as a convectional microchannel design. When limited by temperature, pressure drops are reduced by more than 25%. Finally, the influence of each design variable on the thermal resistance and pumping power was investigated by employing the SHapley Additive exPlanations technique. Overall, we have demonstrated that the proposed framework has merit and can be used as a viable methodology in microchannel heat sink design optimization.

Ongoing risks from climate change have impacted the livelihood of global nomadic communities, and are likely to lead to increased migratory movements in coming years. As a result, mobility considerations are becoming increasingly important in energy systems planning, particularly to achieve energy access in developing countries. Advanced Plug and Play control strategies have been recently developed with such a decentralized framework in mind, more easily allowing for the interconnection of nomadic communities, both to each other and to the main grid. In light of the above, the design and planning strategy of a mobile multi-energy supply system for a nomadic community is investigated in this work. Motivated by the scale and dimensionality of the associated uncertainties, impacting all major design and decision variables over the 30-year planning horizon, Deep Reinforcement Learning (DRL) is implemented for the design and planning problem tackled. DRL based solutions are benchmarked against several rigid baseline design options to compare expected performance under uncertainty. The results on a case study for ger communities in Mongolia suggest that mobile nomadic energy systems can be both technically and economically feasible, particularly when considering flexibility, although the degree of spatial dispersion among households is an important limiting factor. Key economic, sustainability and resilience indicators such as Cost, Equivalent Emissions and Total Unmet Load are measured, suggesting potential improvements compared to available baselines of up to 25%, 67% and 76%, respectively. Finally, the decomposition of values of flexibility and plug and play operation is presented using a variation of real options theory, with important implications for both nomadic communities and policymakers focused on enabling their energy access.

Sampling-based model predictive control (MPC) can be applied to versatile robotic systems. However, the real-time control with it is a big challenge due to its unstable updates and poor convergence. This paper tackles this challenge with a novel derivation from reverse Kullback-Leibler divergence, which has a mode-seeking behavior and is likely to find one of the sub-optimal solutions early. With this derivation, a weighted maximum likelihood estimation with positive/negative weights is obtained, solving by mirror descent (MD) algorithm. While the negative weights eliminate unnecessary actions, that requires to develop a practical implementation that avoids the interference with positive/negative updates based on rejection sampling. In addition, although the convergence of MD can be accelerated with Nesterov's acceleration method, it is modified for the proposed MPC with a heuristic of a step size adaptive to the noise estimated in update amounts. In the real-time simulations, the proposed method can solve more tasks statistically than the conventional method and accomplish more complex tasks only with a CPU due to the improved acceleration. In addition, its applicability is also demonstrated in a variable impedance control of a force-driven mobile robot. https://youtu.be/D8bFMzct1XM

Motion planning and control in autonomous car racing are one of the most challenging and safety-critical tasks due to high speed and dynamism. The lower-level control nodes are expected to be highly optimized due to resource constraints of onboard embedded processing units, although there are strict latency requirements. Some of these guarantees can be provided at the application level, such as using ROS2's Real-Time executors. However, the performance can be far from satisfactory as many modern control algorithms (such as Model Predictive Control) rely on solving complicated online optimization problems at each iteration. In this paper, we present a simple yet effective multi-threading technique to optimize the throughput of online-control algorithms for resource-constrained autonomous racing platforms. We achieve this by maintaining a systematic pool of worker threads solving the optimization problem in parallel which can improve the system performance by reducing latency between control input commands. We further demonstrate the effectiveness of our method using the Model Predictive Contouring Control (MPCC) algorithm running on Nvidia's Xavier AGX platform.